Nomenclature
a 
wavespeed 
A 
crosssectional flow area of a pipe 
BM 
compatibility equations parameter for method of characteristics 
BP 
compatibility equations parameter for method of characteristics 
CD 
discharge coefficient 
CM 
compatibility equations parameter for method of characteristics 
CP 
compatibility equations parameter for method of characteristics 
CV 
valve coefficient 
CHW 
HazenWilliams factor 
D 
diameter of a pipe 
E 
modulus of elasticity 
e 
pipe wall thickness 
f 
friction factor 
fT 
turbulent friction factor (used by Crane, 1988) 
fL 
laminar friction factor 
fTr 
transition friction factor 
F 
error value in mass balance 
FB 
Dimensionless pump torque parameter (see Four Quadrant Model Overview) 
FH 
Dimensionless pump head parameter (see Four Quadrant Model Overview) 
g 
gravitational constant 
H 
head 
HGL 
hydraulic gradeline (piezometric head) 
I 
moment of inertia of pump and entrained liquid 
J 
Jacobian matrix 
K 
loss factor 
K 
constant for Power Law fluid 
KB 
liquid bulk modulus of elasticity 
Ksprinkler 
fire sprinkler loss factor 
L 
length of a pipe 
mass flow rate 

n 
general constant 
n 
constant for Power Law fluid 
N 
pump synchronous speed (rpm) 
P 
pressure, static 
Po 
pressure, stagnation 
Pw 
wetted perimeter 
P 
power 
Q 
volumetric flow rate 
r 
radius 
r 
relaxation 
R, R’ 
resistance or gas constant 
Rc 
coefficient of rigidity 
Re 
Reynolds Number 
s 
pump speed 
SB 
parameter as derived from conservation of mass 
SC 
parameter as derived from conservation of mass 
Sy 
yield stress 
t 
time 
T 
torque on pump 
v 
pump flow ratio to reference 
V 
velocity 
V 
volumex distance along pipe centerline 
z 
elevation 
α, μ, θ 
angle 
α 
pump speed ratio 
β 
diameter ratio 
β 
torque ratio 
λ 
method of characteristics multiplier 
η 
efficiency 
ν 
kinematic viscosity 
ε 
roughness 
ω 
pump speed 
ρ 
density 
μ 
dynamic viscosity 
Subscripts
i 
junction or pipe station at which solution is sought 
j 
junctions with pipes connecting to junction i 
R 
rated conditions for a pump, usually BEP 
o 
stagnation 
∞ 
infinity, far away, ambient 
new 
current time for computation 
old 
most recent time for computation 